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* Inspeaking of ''WorldOfWarcraft'', during the famous "Leeroy Jenkins" video, someone is asked to do a number crunch to calculate their odds of finishing an encounter. [[PoesLaw It's actually not as simple as that - it was done to make fun of guilds]] as well as straw vulcans who may often rely on statistical fallacies.
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* Inspeaking Speaking of ''WorldOfWarcraft'', during the famous "Leeroy Jenkins" "LeeroyJenkins" video, someone is asked to do a number crunch to calculate their odds of finishing an encounter. [[PoesLaw It's actually not as simple as that - it was done to make fun of guilds]] as well as straw vulcans {{Straw Vulcan}}s who may often rely on statistical fallacies.
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* The {{Fox News Channel}}'s fondness for flashy graphics to engage the viewer's attention occasionally lends itself to a few mistakes. Such as [[http://pics.blameitonthevoices.com/112009/fox_news_math_fail.jpg a pie chart where the total breakdowns add up to 193%]], or [[http://www.mathfail.com/scientists-poll.jpg this poll with a breakdown that adds up to 120%]]. Either with the pressure of the rush to get on-screen information ready by showtime, those responsible have little time to double-check their work; or, [[TheyJustDidntCare they care more about making a quick impression on the viewer than ensuring accurate information]].
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** That probably wouldn't have helped. People are ''horrible'' at generating random numbers, so even if she picked equal numbers of black and white cards, a more sophisticated analysis of her picks would reveal what she was doing, most likely by identifying a lack of runs of a single color (see fallacy #2 above).
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** That probably wouldn't might not have helped. People are ''horrible'' at generating random numbers, so even if she picked equal (or near-equal) numbers of black and white cards, a more sophisticated analysis of her picks would reveal what she was doing, most likely by identifying a lack of runs of a single color (see fallacy #2 above).
above). It might ''delay'' the recognition of her ability, though...and unless it were ''blatantly'' obvious what she was doing, it might leave enough doubt to prevent others from being certain.
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* A high school science teacher on ''TheDailyShow'' [[http://www.thedailyshow.com/video/index.jhtml?videoId=225921&title=Large-Hadron-Collider thought there was a 50/50 chance]] of the LHC creating a black hole and causing TheEndOfTheWorldAsWeKnowIt. His rationale? It could happen, or it couldn't happen, therefore there was a 1 in 2 chance of the apocalypse. YouFailNuclearPhysicsForever is also involved.
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* A high school science teacher on ''TheDailyShow'' ''Series/TheDailyShow'' [[http://www.thedailyshow.com/video/index.jhtml?videoId=225921&title=Large-Hadron-Collider thought there was a 50/50 chance]] of the LHC creating a black hole and causing TheEndOfTheWorldAsWeKnowIt. His rationale? It could happen, or it couldn't happen, therefore there was a 1 in 2 chance of the apocalypse. YouFailNuclearPhysicsForever is also involved.
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**Also commonly used by wrestling commentators when discussing multi-person matches. They frequently claim that the champion in a 4-way match only has a 25% chance of retaining his title, with no regard to comparative skill levels or possible alliances between the participants. Of course, since the outcome is predetermined, it tends to be much more common for the champion to retain his belt. These sort of statistical predictions are even more stupid in matches like the elimination chamber where the final competitor to be released would clearly have a huge advantage if other other factors were equal.
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* '''[[GamblersFallacy The Gambler's fallacy]]''': All probabilities should somehow "even out" while you're playing. For example, if the computer has a hit chance of 50%, and hits, that's okay. However, if it then scores another hit right away, TheComputerIsACheatingBastard. In truth, it just happened to be the way the "dice" fell. As is often stated, "Dice have no memory."
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* '''[[GamblersFallacy The Gambler's fallacy]]''': All probabilities should somehow "even out" while you're playing. For example, if the computer has a hit chance of 50%, and hits, that's okay. However, if it then scores another hit right away, TheComputerIsACheatingBastard. In truth, it just happened to be the way the "dice" fell. As is often stated, "Dice "dice have no memory."
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* ''FinalFantasyTacticsA2'': many people report that attacks that give a 95% success rate fail often. It seems likely that this is the case given the number of complaints (especially since the previous game didn't have these problems) but obviously it's impossible to say for sure.
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* ''FinalFantasyTacticsA2'': many people report that attacks that give a 95% success rate fail often. It seems likely that this is the case given the number of complaints (especially since the previous game didn't have these problems) problems - then again, the previous game had an actual flaw in its RNG where success rates tend to be universally higher than the shown numbers suggest) but obviously it's impossible to say for sure.
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Completely untrue. Basic card counting is fairly simple. In fact you can get better than 50% odds just by following some very basic rules about how to play, but the gains are so small as to not be that big of a deal for the casino. It is true that actually making big money off Black Jack is quite difficult and will likely get you thrown out, but that is different.
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*** In Black Jack, it requires card counting (and maximizing your bet when the odds are slightly in your favor), and they'll kick you out if you try it.[[hottip:*:Not only is card counting absurdly difficult to do in the first place (and outright next-to-impossible for people who aren't either Rain-Man-esque savants or ''excellent'' at math), it also tends to involve certain characteristic behaviors that casino dealers are trained to recognize.]] Or they'll reshuffle the deck frequently in the case of Atlantic City casinos, where they can't kick you out. There are also special table rules that messes the available strategies up, like the house hitting on soft 17.
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*** In Black Jack, it requires card counting (and maximizing your bet when the odds are slightly in your favor), and they'll kick you out if you try it.[[hottip:*:Not only is card counting absurdly difficult to do in the first place (and outright next-to-impossible for people who aren't either Rain-Man-esque savants or ''excellent'' at math), it also tends to involve certain characteristic behaviors that casino dealers are trained to recognize.]] Or they'll reshuffle the deck frequently in the case of Atlantic City casinos, where they can't kick you out. There are also special table rules that messes the available strategies up, like the house hitting on soft 17.
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** This one-land-per-two-cards sorting prior to the deck shuffling is accepted practice in tournaments, provided that they are spread blindly vis-a-vis the remaining cards. Any further stacking of the cards is usually frowned upon, such as placing a Dark Ritual right next to each one of your Hypnotic Specters.
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** If your original lost bet is 1 dollar and you follow this strategem, an unlucky streak of 10 consecutive losses has you betting 1024 dollars to chase after your original loss of a ''single dollar''. Even if you do win, all you get is your original dollar back. You were better off just betting one dollar at a time and hoping for a winning streak.
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* In the ''Asterix'' album ''Le Devin'', a centurion is tasked by the roman empire to round up all prophets and soothsayers in order to curb down pagan beliefs that go against roman pantheon beliefs. A conman passing himself as a soothsayer gets caught, and is given a test to see if he can predict a roll of two six-sided dice. He breathes a sigh a relief as he knows his luck is usually awful, and picks (stupidly, statistically speaking) seven, which just so happens to come up on the dice and "prove" him the real deal. He goes on an InsaneTrollLogic demonstration that he picked the right number ''because'' he can't tell the future and confuses the centurion so much that he successfully proves himself a conman rather than a soothsayer.
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* The programmers of ''SidMeyersAlphaCentauri'' fell afoul of this trope when they wrote the code to estimate the battle odds displayed before a combat: they used an obvious-but-wrong method of working out chained probabilities, leading to the game tending to grossly underestimate the actual odds of victory. For example, a strength-8 unit with 30 hitpoints attacking a strength 8 unit with 10 hitpoints would be shown as having a 75% chance of victory; the actual odds of winning are 99.93%. Under the right circumstances, this could result in the game predicting a one-in-a-million chance of winning, when the actual odds are 90%.
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Corrected the most likely outcomes of the sum of 2 six sided dice from \'6, 7, or 9\' to \'6, 7, or 8\'
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* Any game of chance - but most especially any game which uses dice - will find players who think the ''right'' decision is the decision that agrees with the dice as they rolled after they have rolled. For example, in {{Monopoly}}, you may decide to build houses when you see your opponent will land on your monopoly a throw of 6, 7, or 9 on two six-sided dice. Anyone with half a clue as to how the game works and basic probability theory realizes that's about as lethal a situation as your opponent could be in (for a single monopoly), and would build. Yet if your opponent throws a 12, and bypasses your entire trap, your decision was just as reasonable as before. It just didn't pan out. This sort of fallacious thinking holds for:
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* Any game of chance - but most especially any game which uses dice - will find players who think the ''right'' decision is the decision that agrees with the dice as they rolled after they have rolled. For example, in {{Monopoly}}, you may decide to build houses when you see your opponent will land on your monopoly a throw of 6, 7, or 9 8 on two six-sided dice. Anyone with half a clue as to how the game works and basic probability theory realizes that's about as lethal a situation as your opponent could be in (for a single monopoly), and would build. Yet if your opponent throws a 12, and bypasses your entire trap, your decision was just as reasonable as before. It just didn't pan out. This sort of fallacious thinking holds for:
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** The interviewer then suggested that he and the teacher try to breed after the end. The teacher replied that this was impossible, as both were male, but the interviewer insisted it would either happen or not happen, a one-in-two chance!
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** The interviewer Correspondent JohnOliver, who was conducting the interview, then suggested that he and the teacher try to breed after the end. The teacher replied that this was impossible, as both were male, but the interviewer Oliver insisted it would either happen or not happen, a one-in-two chance!
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What on Earth?
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[[AC:FanFic]]
* In Tilman Stieve's ''Tales of The Twilight Menshivik'' stories, Mystique and Val Cooper have an affair, both as women and when Mystique has shapeshifted into a man. Val ends up getting pregnant (much as WordOfGod has said did ''not'' happen with Mystique and Destiny in the 616-verse), and when she informs the rest of X-Factor that her conceiving was "something like a chance in a million"; Strong Guy (Guido Carrosella) replies that for X-teams, "Million-to-one chances crop up nine times out of ten."
** ...which is a line stolen from Terry Pratchett's Discworld series.
** While that line is amusing, it's not inherently wrong. When randomly choosing a number from zero to a million, ''all'' of the possibilities have million to one odds against them. In that case, million-to-one will chances crop up ''ten'' times out of ten. You just can't predict ''which'' million-to-one chance will actually occur. Thus, the actual implication of the line is that there are many possibilities, none of which are likely.
*** In the example given, there's ''two'' possibilities, the other of which is ''not'' being pregnant.
*** That's not really valid, because it's not a 50/50 distribution. Most of the time when a woman has sex, she doesn't become pregnant.
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* Statistics on {{Discworld}} work.... different. When something has a million to one chance (someone has to point out it has a million to one chance), it will (most) definitely(!) work. Some people try to lower the odds, since a 50% chance still is a 50% chance, and also a 1% chance is much worse than the aforementioned million to one.
** Maybe. This was codified in ''Discworld/GuardsGuards'', but the million-to-one shot there ''didn't work'' with the narration noting that "Chance, who can sometimes overrule even the gods, has 999,999 casting votes".
*** The ''reason'' it didn't work is that they were trying to manipulate the chance to become 1,000,000 to one, but came only as close as 984,876 to one. Also, The Lady does not like being invoked intentionally.
*** Yes, but the odds of surviving the aforementioned situation was exactly a million to one, so it still sort of worked out for the characters.
*** Wasn't the real reason for failure that they were aiming for the 'voonerables' (impliedly [[GroinAttack men's most sensitive area]]) on a ''FEMALE'' dragon, meaning their chance was technically zero?
** ''Discworld/TheScienceOfDiscworld'' books have an arguably accurate but somewhat twisted take on statistics: the chances of ''anything at all'' happening are so remote that it doesn't make sense to be surprised at ''specific'' unlikely things.
** Maybe. This was codified in ''Discworld/GuardsGuards'', but the million-to-one shot there ''didn't work'' with the narration noting that "Chance, who can sometimes overrule even the gods, has 999,999 casting votes".
*** The ''reason'' it didn't work is that they were trying to manipulate the chance to become 1,000,000 to one, but came only as close as 984,876 to one. Also, The Lady does not like being invoked intentionally.
*** Yes, but the odds of surviving the aforementioned situation was exactly a million to one, so it still sort of worked out for the characters.
*** Wasn't the real reason for failure that they were aiming for the 'voonerables' (impliedly [[GroinAttack men's most sensitive area]]) on a ''FEMALE'' dragon, meaning their chance was technically zero?
** ''Discworld/TheScienceOfDiscworld'' books have an arguably accurate but somewhat twisted take on statistics: the chances of ''anything at all'' happening are so remote that it doesn't make sense to be surprised at ''specific'' unlikely things.
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* Statistics on {{Discworld}} work.... different. When something has a million to one chance (someone has to point out it has a million to one chance), it will (most) definitely(!) work. Some people try to lower the odds, since a 50% chance still is a 50% chance, and also a 1% chance is much worse than the aforementioned million to one.
** Maybe. This was codified in ''Discworld/GuardsGuards'', but the million-to-one shot there ''didn't work'' with the narration noting that "Chance, who can sometimes overrule even the gods, has 999,999 casting votes".
*** The ''reason'' it didn't work is that they were trying to manipulate the chance to become 1,000,000 to one, but came only as close as 984,876 to one. Also, The Lady does not like being invoked intentionally.
*** Yes, but the odds of surviving the aforementioned situation was exactly a million to one, so it still sort of worked out for the characters.
*** Wasn't the real reason for failure that they were aiming for the 'voonerables' (impliedly [[GroinAttack men's most sensitive area]]) on a ''FEMALE'' dragon, meaning their chance was technically zero?
**''Discworld/TheScienceOfDiscworld'' books have an arguably accurate but somewhat twisted take on statistics: the chances of ''anything at all'' happening are so remote that it doesn't make sense to be surprised at ''specific'' unlikely things.
** Maybe. This was codified in ''Discworld/GuardsGuards'', but the million-to-one shot there ''didn't work'' with the narration noting that "Chance, who can sometimes overrule even the gods, has 999,999 casting votes".
*** The ''reason'' it didn't work is that they were trying to manipulate the chance to become 1,000,000 to one, but came only as close as 984,876 to one. Also, The Lady does not like being invoked intentionally.
*** Yes, but the odds of surviving the aforementioned situation was exactly a million to one, so it still sort of worked out for the characters.
*** Wasn't the real reason for failure that they were aiming for the 'voonerables' (impliedly [[GroinAttack men's most sensitive area]]) on a ''FEMALE'' dragon, meaning their chance was technically zero?
**
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** Regression to the Mean overall is fueled by a misunderstanding of statistics, and has many (sometimes serious) consequences. "You say Homeopathy/Acupuncture/pseudoscience of your choice worked for your arthritis pain? Wow. When did you take it? When you felt at your worst? Did it ever occur to you that short of ''trying'' to make things worse, you would almost certainly feel better after hitting rock bottom? Does "nowhere to go but up" mean anything?"
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** Regression to the Mean overall is fueled by a misunderstanding of statistics, and has many (sometimes serious) consequences. "You say Homeopathy/Acupuncture/pseudoscience of your choice worked for your arthritis pain? Wow. When did you take it? When you felt at your worst? worst. Did it ever occur to you that short of ''trying'' to make things worse, you would almost certainly feel better a while after hitting rock bottom? Does "nowhere to go but up" mean anything?"
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** Regression to the Mean overall is fueled by a misunderstanding of statistics, and has many (sometimes serious) consequences. "You say Homeopathy/Acupuncture/pseudoscience of your choice worked for your arthritis pain? Wow. When did you take it? When you felt at your worst? Did it ever occur to you that short of ''trying'' to make things worse, you would almost certainly feel better after hitting rock bottom? Does "nowhere to go but up" mean anything?"
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Shuffled around the text for clarity. Casino should be at a higher level than Craps.
Changed line(s) 39,43 (click to see context) from:
* While most casino games are set up to take money from statistics failers over the long haul, the side bets on ''Craps'' tables are particularly blatant, because the fair odds are so simple to calculate. For example, the odds of rolling two sixes are 1/6 * 1/6 = 1/36 (1:35 odds), but the payoff on that side bet is 30:1.
** Most casino games? Make that (almost) ''all''. If they weren't, the casino would lose money in the long run, and why would they do that? (Poker is an exception in so far as you aren't playing against the casino but your fellow players - there, the casino makes money through rakes of the pot and fees.)
*** Technically, there are two single player casino games which sometimes offer a theoretical gain to the player (and loss to the casino). Video Poker, and Blackjack. In the case of Video Poker, the advantage is extremely small, if present at all, and is more than canceled out by a player occasionally misplaying due to tiredness or a mistake or whatever. On average, it takes three solid years of perfect play to break even. In the case of Blackjack, it requires card counting (and maximizing your bet when the odds are slightly in your favor), and they'll kick you out if you try it.[[hottip:*:Not only is card counting absurdly difficult to do in the first place (and outright next-to-impossible for people who aren't either Rain-Man-esque savants or ''excellent'' at math), it also tends to involve certain characteristic behaviors that casino dealers are trained to recognize.]] Or they'll reshuffle the deck frequently in the case of Atlantic City casinos, where they can't kick you out.
*** And that's true of Blackjack only as long as you play ''perfect'' basic strategy consistently on a standard version game without special table rules. House hitting on soft 17 reduces long haul payback just slightly under 100%.
** The one fair bet in Craps, the free-odds wager, pays a fair, proportional amount should you win. That said, there is no space on the Craps table for it (the player has to "know" to place it at the right time), and it can only be placed as a supplement to your original bet (which ''is'' subject to the house percentage.)
** Most casino games? Make that (almost) ''all''. If they weren't, the casino would lose money in the long run, and why would they do that? (Poker is an exception in so far as you aren't playing against the casino but your fellow players - there, the casino makes money through rakes of the pot and fees.)
*** Technically, there are two single player casino games which sometimes offer a theoretical gain to the player (and loss to the casino). Video Poker, and Blackjack. In the case of Video Poker, the advantage is extremely small, if present at all, and is more than canceled out by a player occasionally misplaying due to tiredness or a mistake or whatever. On average, it takes three solid years of perfect play to break even. In the case of Blackjack, it requires card counting (and maximizing your bet when the odds are slightly in your favor), and they'll kick you out if you try it.[[hottip:*:Not only is card counting absurdly difficult to do in the first place (and outright next-to-impossible for people who aren't either Rain-Man-esque savants or ''excellent'' at math), it also tends to involve certain characteristic behaviors that casino dealers are trained to recognize.]] Or they'll reshuffle the deck frequently in the case of Atlantic City casinos, where they can't kick you out.
*** And that's true of Blackjack only as long as you play ''perfect'' basic strategy consistently on a standard version game without special table rules. House hitting on soft 17 reduces long haul payback just slightly under 100%.
** The one fair bet in Craps, the free-odds wager, pays a fair, proportional amount should you win. That said, there is no space on the Craps table for it (the player has to "know" to place it at the right time), and it can only be placed as a supplement to your original bet (which ''is'' subject to the house percentage.)
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* While most casino Casino games are set up to take so that over a long period of time, the statistical average favours the house (house advantage or house edge). In {{Poker}}, the bets are fair, since you're playing against other players rather than against the house, but instead the casino makes money from statistics failers over through rakes of the long haul, the pot and fees.
** The side bets on ''Craps'' tables are particularly blatant, because the fair odds are so simple to calculate. For example, the odds of rolling two sixes are 1/6 * 1/6 = 1/36 (1:35 odds), but the payoff on that side bet is 30:1.
** Most casino games? Make that (almost) ''all''. If they weren't, *** The one fair bet in Craps, the casino would lose money in free-odds wager, pays a fair, proportional amount should you win. That said, there is no space on the long run, Craps table for it (the player has to "know" to place it at the right time), and why would they do that? (Poker is an exception in so far it can only be placed as you aren't playing against the casino but a supplement to your fellow players - there, original bet (which ''is'' subject to the casino makes money through rakes of the pot and fees.)
***house percentage.)
** Technically, there aretwo single player casino games which sometimes offer a theoretical gain to the player (and loss to with the casino). Video Poker, and Blackjack. In right strategy. However, since the case of gain is very small, any mistake will set you back a lot.
*** In Video Poker, the advantage is extremely small, if present atall, and is more than canceled out by a player occasionally misplaying due to tiredness or a mistake or whatever. all. On average, it takes three solid years of perfect play to break even. even.
*** Inthe case of Blackjack, Black Jack, it requires card counting (and maximizing your bet when the odds are slightly in your favor), and they'll kick you out if you try it.[[hottip:*:Not only is card counting absurdly difficult to do in the first place (and outright next-to-impossible for people who aren't either Rain-Man-esque savants or ''excellent'' at math), it also tends to involve certain characteristic behaviors that casino dealers are trained to recognize.]] Or they'll reshuffle the deck frequently in the case of Atlantic City casinos, where they can't kick you out.
*** And that's true of Blackjack only as long as you play ''perfect'' basic strategy consistently on a standard version game withoutout. There are also special table rules. House rules that messes the available strategies up, like the house hitting on soft 17 reduces long haul payback just slightly under 100%.
** The one fair bet in Craps, the free-odds wager, pays a fair, proportional amount should you win. That said, there is no space on the Craps table for it (the player has to "know" to place it at the right time), and it can only be placed as a supplement to your original bet (which ''is'' subject to the house percentage.)17.
** The side bets on ''Craps'' tables are particularly blatant, because the fair odds are so simple to calculate. For example, the odds of rolling two sixes are 1/6 * 1/6 = 1/36 (1:35 odds), but the payoff on that side bet is 30:1.
***
** Technically, there are
*** In Video Poker, the advantage is extremely small, if present at
*** In
*** And that's true of Blackjack only as long as you play ''perfect'' basic strategy consistently on a standard version game without
** The one fair bet in Craps, the free-odds wager, pays a fair, proportional amount should you win. That said, there is no space on the Craps table for it (the player has to "know" to place it at the right time), and it can only be placed as a supplement to your original bet (which ''is'' subject to the house percentage.)
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Fixed clumsy writing by yours truly.
Changed line(s) 48 (click to see context) from:
** Because of the green fields on a roulette table, a 0 and sometimes a 00, the chance to win is 18:37 or 18:38, which is less than 50%. Because the expected profit is negative, the sum of many such bets is also negative.
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** Because of the The green fields on a roulette table, a 0 and sometimes also a 00, reduces the chance to win is to 18:37 or 18:38, which is less than 50%. Because the expected profit is negative, the sum of many such bets is also negative.
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Rewrote and removed thread mode.
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* A sure-fire way to win money in Roulette exists but it's tedious. You need a casino (preferably online due to time demand) which gives 2:1 on 1:2 (winning a red or black bet results in double the money back) and is known to pay money out near immediatly. Start with betting 1, if you lose, bet 2, if you lose, bet 4 etc etc. The probability to constantly bet wrong is 0.5^n (n being the amount of bets in that row). You'll win your a plus of your initial bet at some point. Go to betting 1 again once you won and repeat. Only restriction that can happen is a maximum value you can bet.
** This(used to be called Martingale) doesn't work unless you have both an infinite amount of money and time.
** This doesn't actually work since Roulette wheels have two results (0 and 00) which do not count as either red or black so the odds of winning a red or black bid (or the even or odds bids) is actually slightly less than 50%.
*** That is misleading; the strategy of doubling your bet every time you lose will still work since you are bound to win eventually, and at that point you'll have made a profit of one dollar. The real reason this strategy doesn't work in the real world is that there's always a table limit that makes this strategy impossible; the winning probability being less than half merely turns a wager with zero expected payoff ("on average" result for a specific definition of "on average") into a wager with negative expected payoff (aka house edge)
**** No, it's not. You'll lose 1/37 of your initial bet every time you start from the beginning of the process. This is due to the fact that if you limit yourself to n losses in a row, your probability of reaching the limit is (19/37)^n whilst your loss at that point is 2^n. Saying you'll always eventually win is a fallacy unless you've managed to amass 2^(infinity) units of currency.
** This(used to be called Martingale) doesn't work unless you have both an infinite amount of money and time.
** This doesn't actually work since Roulette wheels have two results (0 and 00) which do not count as either red or black so the odds of winning a red or black bid (or the even or odds bids) is actually slightly less than 50%.
*** That is misleading; the strategy of doubling your bet every time you lose will still work since you are bound to win eventually, and at that point you'll have made a profit of one dollar. The real reason this strategy doesn't work in the real world is that there's always a table limit that makes this strategy impossible; the winning probability being less than half merely turns a wager with zero expected payoff ("on average" result for a specific definition of "on average") into a wager with negative expected payoff (aka house edge)
**** No, it's not. You'll lose 1/37 of your initial bet every time you start from the beginning of the process. This is due to the fact that if you limit yourself to n losses in a row, your probability of reaching the limit is (19/37)^n whilst your loss at that point is 2^n. Saying you'll always eventually win is a fallacy unless you've managed to amass 2^(infinity) units of currency.
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* A sure-fire way to win money One popular strategy (called [[http://en.wikipedia.org/wiki/Martingale_(roulette_system) Martingale]]) in Roulette exists but it's tedious. You need a casino (preferably online due that is believed to time demand) which gives 2:1 always net you money. The same strategy works the same on 1:2 (winning a red or black any 50% chance double money back bets (or as long as the chance to win is balanced against the payout). The basics of the strategy is to bet results in 1 on red/black, odd/even, or high/low when you start and if you win, and double the money back) and is known to pay money out near immediatly. Start with bet if you lose.[[hottip:*:For example, losing three in a row then winning means betting 1, if you lose, bet 2, if you lose, bet 4 etc etc. 4, 8, which means you've lost 7 and won 8, with a net profit of 1.]] The probability to constantly bet wrong belief is 0.5^n (n being the amount of bets in that row). You'll you will eventually win, and thus win your a plus of your the initial bet at some point. Go to betting 1 again once you won and repeat. Only restriction that can happen is bet.\\
There are amaximum value you can bet.
** This(used to be called Martingale)few reasons why this doesn't work unless work:
** To always win, youhave both need an infinite amount of money and time.
**This doesn't actually work since Roulette wheels have two results (0 and 00) In real casinos there is always a betting limit, which do not count as either red or black so removes the odds option to double up at some point.
** Because ofwinning a red or black bid (or the even green fields on a roulette table, a 0 and sometimes a 00, the chance to win is 18:37 or odds bids) 18:38, which is actually slightly less than 50%.
*** That is misleading;50%. Because the strategy of doubling your bet every time you lose will still work since you are bound to win eventually, and at that point you'll have made a profit of one dollar. The real reason this strategy doesn't work in the real world is that there's always a table limit that makes this strategy impossible; the winning probability being less than half merely turns a wager with zero expected payoff ("on average" result for a specific definition of "on average") into a wager with negative expected payoff (aka house edge)
**** No, it's not. You'll lose 1/37 of your initial bet every time you start fromprofit is negative, the beginning sum of the process. This many such bets is due to the fact that if you limit yourself to n losses in a row, your probability of reaching the limit is (19/37)^n whilst your loss at that point is 2^n. Saying you'll always eventually win is a fallacy unless you've managed to amass 2^(infinity) units of currency.also negative.
There are a
** This(used to be called Martingale)
** To always win, you
**
** Because of
*** That is misleading;
**** No, it's not. You'll lose 1/37 of your initial bet every time you start from
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Duplicated below in more detail about why it doesn\'t work.
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*** Although there are ([[AwesomeButImpractical potentially expensive and fairly pointless]]) [[http://www.futilitycloset.com/2009/10/11/jackpot/ ways to ensure a win at a roulette wheel.]]
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** Anyone playing roulette for anything other than costly entertainment
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** Anyone playing roulette for anything other than costly entertainmententertainment.
*** Although there are ([[AwesomeButImpractical potentially expensive and fairly pointless]]) [[http://www.futilitycloset.com/2009/10/11/jackpot/ ways to ensure a win at a roulette wheel.]]
*** Although there are ([[AwesomeButImpractical potentially expensive and fairly pointless]]) [[http://www.futilitycloset.com/2009/10/11/jackpot/ ways to ensure a win at a roulette wheel.]]
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** That probably wouldn't have helped. People are ''horrible'' at generating random numbers, so even if she picked equal numbers of black and white cards, a more sophisticated analysis of her picks would reveal what she was doing, most likely by identifying a lack of runs of a single color (see fallacy #2 above).
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*** And that's true of Blackjack only as long as you play ''perfect'' basic strategy consistently on a standard version game without special table rules. House hitting on soft 17 reduces long haul payback just slightly under 100%.
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** Of course it is [[MetaFiction that kind]] of play so the canonical explanation might well be that Stoppard is doing it.
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whoops
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**** No, it's not. You'll lose 1/37 of your initial bet every time you start from the beginning of the process. This is due to the fact that if you limit yourself to n losses in a row, your probability of reaching the limit is (19/37)^n whilst your loss at that point is (1/2)^n. Saying you'll always eventually win is a fallacy unless you've managed to amass 2^(infinity) units of currency.
to:
**** No, it's not. You'll lose 1/37 of your initial bet every time you start from the beginning of the process. This is due to the fact that if you limit yourself to n losses in a row, your probability of reaching the limit is (19/37)^n whilst your loss at that point is (1/2)^n.2^n. Saying you'll always eventually win is a fallacy unless you've managed to amass 2^(infinity) units of currency.
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correcting a probabilistic misconception :P
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**** No, it's not. You'll lose 1/37 of your initial bet every time you start from the beginning of the process. This is due to the fact that if you limit yourself to n losses in a row, your probability of reaching the limit is (19/37)^n whilst your loss at that point is (1/2)^n. Saying you'll always eventually win is a fallacy unless you've managed to amass 2^(infinity) units of currency.
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Professional =/= Stop Having Fun Guy.
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* This trope is hugely responsible for the ''{{Pokemon}}'' entries on TheComputerIsACheatingBastard, and is the number 1 thing the game's [[StopHavingFunGuys professional]] players complain about to similar levels of usage.
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* This trope is hugely responsible for the ''{{Pokemon}}'' entries on TheComputerIsACheatingBastard, and is the number 1 thing the game's [[StopHavingFunGuys professional]] professional players complain about to similar levels of usage.
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Moved the page to give it a proper rename instead of just the custom title rename.
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[[caption-width-right:346: [[AltText By the third trimester, there will be hundreds of babies inside you.]]]]
->''"There are three kinds of lies: [[LiesDamnedLiesAndStatistics lies, damned lies, and statistics.]]"''
-->--'''BenjaminDisraeli'''
It has been generally demonstrated that, because human brains are wired toward pattern detection, we are lousy at intuitively interpreting statistics; this is the main reason why casinos are viable businesses. Trying to do anything to curb this problem often results in the worship of the RandomNumberGod, or beliefs like:
* '''The hit/miss belief''': "A hit ratio below 25% is hopeless and a hit ratio above 75% is guaranteed. Everything else is a crapshoot."\\
\\
Not so much. There are four groups of 25% in 100%. Go ahead and count them. We'll wait. \\
\\
There is a 1 in 4 chance of hitting any one of them.
* '''[[GamblersFallacy The Gambler's fallacy]]''': All probabilities should somehow "even out" while you're playing. For example, if the computer has a hit chance of 50%, and hits, that's okay. However, if it then scores another hit right away, TheComputerIsACheatingBastard. In truth, it just happened to be the way the "dice" fell. As is often stated, "Dice have no memory."
* '''Naive Combination of probabilities''': Given the probabilities of two events, people will often simply either add them or multiply them. Generally speaking, calculating the combined probability is much more complicated. For example, if someone accused a group of 100 people of taking drugs, each person would be 1%. Accusing 4% of adults, and 4% of children, if the group is half of each, would be 4 people, not 8.
* '''The Definition of Probability''': There's two ways probability can be defined. The first is what should happen in a random process ''in the long run''. The second is the degree of certainty with which a belief is held. The first definition applies to statements like, "The odds of rolling a six on a fair die are one in six." The second applies to statements like, "My favorite team will win this game." This difference can be very important. These two views are called frequentist and Bayesian, respectively.
* '''Decision-Making and Probability''': Many make a mistake related to all these fallacies. When a decision-maker makes a decision to play the odds in a situation where he can calculate the odds, he's taking a measured risk based on what he knows at the time. This is his best decision based on what he could possibly know at the time. If this fails, calling it a ''wrong'' decision is fallacious because it would require knowing the less-likely alternative would happen. For example, if two gamblers agree to roll a fair die, betting 1:1 where Gambler A wins on a 1-5, and Gambler B wins on a 6, Gambler B is making an idiotic decision to bet - and the decision remains idiotic even in hindsight if he wins.
Note that while this often makes fun of the developers messing up at statistics or the author having no clue how it works, this can actually be invoked or justified.
Also see TwentyPercentMoreAwesome, which involves quantifying the unquantifiable.
----
!! Examples of how this plays out in storytelling:
[[AC:Card and Dice Games]]
* Any game of chance - but most especially any game which uses dice - will find players who think the ''right'' decision is the decision that agrees with the dice as they rolled after they have rolled. For example, in {{Monopoly}}, you may decide to build houses when you see your opponent will land on your monopoly a throw of 6, 7, or 9 on two six-sided dice. Anyone with half a clue as to how the game works and basic probability theory realizes that's about as lethal a situation as your opponent could be in (for a single monopoly), and would build. Yet if your opponent throws a 12, and bypasses your entire trap, your decision was just as reasonable as before. It just didn't pan out. This sort of fallacious thinking holds for:
** Naive poker players, who fold a bad hand only to see it turn around later (in a game with community cards)
** Players of any RPG, when a character fails at a good plan due to some really off-the-wall lousy rolls or succeeds at an absurd plan through sheer dumb luck
** Board game players who fall into the type of thinking in the ''Monopoly'' example
** Wargamers who misinterpret why some of their opponents quickly calculate odds, then make their decisions based on what's likely to occur from a particular gambit
** Anyone playing roulette for anything other than costly entertainment
* Many {{Bridge}} players feel that the computer-generated hands used for many duplicate games are more unusual (i.e. favor more unlikely distribution of cards) than human-shuffled hands. They're right, but in a backwards way: The computer-generated hands are ''more likely to be completely random'' than hands dealt from a human-shuffled deck. Even the best human-shuffled deck will retain a few cards in the same relative order as they were played in the last hand; computer-generated hands don't (except at the frequency you'd expect from random chance).
* Many players of the online version of ''MagicTheGathering'' are convinced that the algorithm used to shuffle players' decks is flawed and is biased. (Some say the bias is towards "mana flood", where you get too many mana-producing cards (and not enough spells to actually use that mana with), while others say towards "mana screw", which is ''the exact opposite'' -- not getting enough.) In reality, the algorithm is completely incapable of either, since it does not consider what type any given card is when performing the shuffle. The reason for the dissonance between physical and online play (when there is one at all -- mana screw and mana flood are common on cardboard too) is that having to physically shuffle a deck enough to provide a truly random distribution every time would be ''incredibly annoying'', particularly given the number of times some decks end up being shuffled in a single game. Most people just take their land cards, which end up all in one pile at the end of a game and put them into the deck at fairly even intervals to avoid there being giant clumps of nothing but land. For practical reasons, even in tournaments it's accepted that the deck doesn't have to be truly randomly distributed -- it just needs to be random enough that a player can't predict what comes next.
* Go to any online {{poker}} forum and look in the General Discussion forum. More often then not, you'll find a sticky about the game not being rigged, and an explanation of why it may seem that it is. Of course, most forums will also have a 'Bad Beats' section for whining about said 'rigged' play screwing the loser... (never mind that they were chasing a flush draw and getting really poor pot odds on the call...)
** In professional (off-line) poker tournaments, the dealer start to shuffle every new deck by simply scattering the cards on the table and mixing them around (similar to how one would shuffle dominoes). ''Then'' the cards are loaded into whatever shuffling device is used. (This type of shuffle is commonly called a Beginner's or Corgi shuffle.)
*** If you're interested, in the UK this shuffle is known as a 'chemmy' (pronounced shemmy), named after the game 'chemin-de-fer' made popular in French casinos, but known to most as the game Baccarat seen in a number of James Bond movies.
* While most casino games are set up to take money from statistics failers over the long haul, the side bets on ''Craps'' tables are particularly blatant, because the fair odds are so simple to calculate. For example, the odds of rolling two sixes are 1/6 * 1/6 = 1/36 (1:35 odds), but the payoff on that side bet is 30:1.
** Most casino games? Make that (almost) ''all''. If they weren't, the casino would lose money in the long run, and why would they do that? (Poker is an exception in so far as you aren't playing against the casino but your fellow players - there, the casino makes money through rakes of the pot and fees.)
*** Technically, there are two single player casino games which sometimes offer a theoretical gain to the player (and loss to the casino). Video Poker, and Blackjack. In the case of Video Poker, the advantage is extremely small, if present at all, and is more than canceled out by a player occasionally misplaying due to tiredness or a mistake or whatever. On average, it takes three solid years of perfect play to break even. In the case of Blackjack, it requires card counting (and maximizing your bet when the odds are slightly in your favor), and they'll kick you out if you try it.[[hottip:*:Not only is card counting absurdly difficult to do in the first place (and outright next-to-impossible for people who aren't either Rain-Man-esque savants or ''excellent'' at math), it also tends to involve certain characteristic behaviors that casino dealers are trained to recognize.]] Or they'll reshuffle the deck frequently in the case of Atlantic City casinos, where they can't kick you out.
** The one fair bet in Craps, the free-odds wager, pays a fair, proportional amount should you win. That said, there is no space on the Craps table for it (the player has to "know" to place it at the right time), and it can only be placed as a supplement to your original bet (which ''is'' subject to the house percentage.)
* A sure-fire way to win money in Roulette exists but it's tedious. You need a casino (preferably online due to time demand) which gives 2:1 on 1:2 (winning a red or black bet results in double the money back) and is known to pay money out near immediatly. Start with betting 1, if you lose, bet 2, if you lose, bet 4 etc etc. The probability to constantly bet wrong is 0.5^n (n being the amount of bets in that row). You'll win your a plus of your initial bet at some point. Go to betting 1 again once you won and repeat. Only restriction that can happen is a maximum value you can bet.
** This(used to be called Martingale) doesn't work unless you have both an infinite amount of money and time.
** This doesn't actually work since Roulette wheels have two results (0 and 00) which do not count as either red or black so the odds of winning a red or black bid (or the even or odds bids) is actually slightly less than 50%.
*** That is misleading; the strategy of doubling your bet every time you lose will still work since you are bound to win eventually, and at that point you'll have made a profit of one dollar. The real reason this strategy doesn't work in the real world is that there's always a table limit that makes this strategy impossible; the winning probability being less than half merely turns a wager with zero expected payoff ("on average" result for a specific definition of "on average") into a wager with negative expected payoff (aka house edge)
* There is an optional "Event Deck" for the board game ''{{Settlers of Catan}}''. Using it instead of the dice makes probabilities "even out" somewhat (going through most of the deck before reshuffling guarantees that each number will come up about as often as it "should").
[[AC:FanFic]]
* In Tilman Stieve's ''Tales of The Twilight Menshivik'' stories, Mystique and Val Cooper have an affair, both as women and when Mystique has shapeshifted into a man. Val ends up getting pregnant (much as WordOfGod has said did ''not'' happen with Mystique and Destiny in the 616-verse), and when she informs the rest of X-Factor that her conceiving was "something like a chance in a million"; Strong Guy (Guido Carrosella) replies that for X-teams, "Million-to-one chances crop up nine times out of ten."
** ...which is a line stolen from Terry Pratchett's Discworld series.
** While that line is amusing, it's not inherently wrong. When randomly choosing a number from zero to a million, ''all'' of the possibilities have million to one odds against them. In that case, million-to-one will chances crop up ''ten'' times out of ten. You just can't predict ''which'' million-to-one chance will actually occur. Thus, the actual implication of the line is that there are many possibilities, none of which are likely.
*** In the example given, there's ''two'' possibilities, the other of which is ''not'' being pregnant.
*** That's not really valid, because it's not a 50/50 distribution. Most of the time when a woman has sex, she doesn't become pregnant.
[[AC: {{Literature}}]]
* Statistics on {{Discworld}} work.... different. When something has a million to one chance (someone has to point out it has a million to one chance), it will (most) definitely(!) work. Some people try to lower the odds, since a 50% chance still is a 50% chance, and also a 1% chance is much worse than the aforementioned million to one.
** Maybe. This was codified in ''Discworld/GuardsGuards'', but the million-to-one shot there ''didn't work'' with the narration noting that "Chance, who can sometimes overrule even the gods, has 999,999 casting votes".
*** The ''reason'' it didn't work is that they were trying to manipulate the chance to become 1,000,000 to one, but came only as close as 984,876 to one. Also, The Lady does not like being invoked intentionally.
*** Yes, but the odds of surviving the aforementioned situation was exactly a million to one, so it still sort of worked out for the characters.
*** Wasn't the real reason for failure that they were aiming for the 'voonerables' (impliedly [[GroinAttack men's most sensitive area]]) on a ''FEMALE'' dragon, meaning their chance was technically zero?
** ''Discworld/TheScienceOfDiscworld'' books have an arguably accurate but somewhat twisted take on statistics: the chances of ''anything at all'' happening are so remote that it doesn't make sense to be surprised at ''specific'' unlikely things.
* DaveBarry once joked that he always flew on the airline with the most recent crash, on the assumption that it wouldn't be "due" for another one.
* MarkTwain's ''Life on the Mississippi'' contained the following proof of what you can do with statistics:
--> In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.
* In [[LoisDuncan Lois Duncan's]] ''Literature/AGiftOfMagic'', the psychic protagonist, Nancy, is given a standard test to detect telepathic abilities. She is asked to pick, without looking, all the white cards out of a deck of cards filled with an equal amount of black and white cards. Because she wishes to hide her ability, she picks all the black cards so that she would get all the "wrong" answers and fail the test. The examiner sees right through Nancy's ploy because there is an equal probability of picking only white or only black cards and explains that if she really wanted to screw up the test, she should have picked a roughly equal amount of black and white cards at random.
[[AC: LiveActionTV]]
* A high school science teacher on ''TheDailyShow'' [[http://www.thedailyshow.com/video/index.jhtml?videoId=225921&title=Large-Hadron-Collider thought there was a 50/50 chance]] of the LHC creating a black hole and causing TheEndOfTheWorldAsWeKnowIt. His rationale? It could happen, or it couldn't happen, therefore there was a 1 in 2 chance of the apocalypse. YouFailNuclearPhysicsForever is also involved.
** The interviewer then suggested that he and the teacher try to breed after the end. The teacher replied that this was impossible, as both were male, but the interviewer insisted it would either happen or not happen, a one-in-two chance!
* In the ''Series/CornerGas'' episode "Security Cam", Karen figures that there's a 50% chance of a riot breaking out in downtown Dog River, using exactly the same reasoning.
* On ''TheOReillyFactor'', Bill O'Reilly argued that life expectancy was lower in the US than in Canada because the US has ten times as many people, and therefore has ten times the [[http://mediamatters.org/mmtv/200907270052 number of accidents.]]
* On the second episode of ''BurnNotice'', Michael guessed that a conman's former cellmate didn't drink, which made some sense in the context if he was genre savvy to those sorts of questions, but his explanation didn't: that he just guessed because the man either drank or he didn't, a fifty percent chance. So either Michael's estimate of teetotalers among the male prisoner population is extremely optimistic, or he needs to take a stats class.
** A bit more complicated: from the way the conversation was going, it was clear that the conman was testing Michael on whether he really knew the former cellmate. So the odds weren't whether the cellmate was a drinker, but whether the comment about the drinking was a "test question" or not.
* A common mention on the show ''Series/HellsKitchen,'' as well as a number of other reality shows, is that at any given time a given contestant has a 1 in X chance of winning the grand prize, where X is the number of remaining contestants. Not only does this suggest that the winner is chosen at random (which is not the intent of the statement), but also that every contestant is equally likely to win. This is untrue, especially on shows which have a number of obvious dud contestants (such as ''Hell's Kitchen'').
* In the ''LawAndOrder'' episode "Coma", [=McCoy=] tries to ease Kincaid's conscience about subjecting a comatose victim to a high-risk surgery in order to remove a possibly trial-winning bullet. Subverted in that he's perfectly aware that it's bad statistics.
-->''"Well, I see one of three things happening: she gets better, she gets worse, she stays the same, and we get strong evidence. Two out of three ain't bad."''
* Invoked in ''{{Survivor}}'' - As the players in the game dwindle, Probst tells them that they have a "one in ''x'' shot at winning the million dollars." The way he mentions this, it sounds like the winner of challenges (and at the game ''period'') is chosen at random, when it actually isn't. (You can argue that if you're in the final six with TheLoad and someone who the jury ''hates'', you would have a one in ''four'' shot since the jurors would not vote for them.) Justified in that he [[FridgeBrilliance does this to motivate the players]], and it's part of his "character".
[[AC:[=RPG=]s, [=MMORPG=]s, and other VideoGames]]
* MMO players, almost without fail, will adhere to mindset two - they will notice the streak of resists/misses/landed enemy attacks/what have you that killed or almost killed them, but never notice the long, long, long string of hits that precede it. Any and all MMO forums will have a topic pop up fairly regularly asking whether (or sometimes screaming loudly even with no evidence to that effect other than they had a string of bad luck) the RNG is broken.
** ...which can lead to [[FinalFantasyXI no small confusion]] at times.
** To further complicate things, some [=MMOs=] actually ''do'' use a skewed RNG, precisely because true randomness could, in theory, result in a string of misses one real day long, or the opposite. Since [=MMOs=] rely on a very ''predictable'' form of randomness (e.g., no plucky level 1 can be able to beat a level 20 monster because the monster miraculously rolls no hits, but if attacking a level 4 he must be able to win through pure luck some of the time), various measures can be put in place to make sure the game generates the good, reliable sort of random.
* All ''FireEmblem'' games after the fifth display inaccurate hit/miss percentages. The game actually uses the average of two random numbers to determine a hit, so a 75% chance to hit is really 87.5%. This system is likely in place to make [[FragileSpeedster dodging-type]] units evade more (and thus more viable) and high-accuracy characters strike more and lessens the chance that such a character dies ([[AntiFrustrationFeatures Due to permanent death and limited saving, this means restarting the entire level in most games]]) against all 3 of the random mooks that has a 2% chance to hit each.
** To prevent SaveScumming abuse, the 10th game's (unlike the 9th's, which was completely random) bonus experience system [[hottip:*:EXP that may be freely given to any unit between levels, helpful for raising MagikarpPower characters, getting that precious extra level of stats ups or helping the guy lagging behind]] will ''always'' increases a character's 3 stats with the highest growth rate (Has an x percent chance to raise this stats on every level up). This wound up making it ''more'' broken, as some units quickly hit the {{Cap}} on their main stats (Aran), causing stats that would other almost never grow to suddenly increase at insane rates.
** Starting with the 10th, if a character does not get at least one stats increased during a level up, the game rerolls (unless a character has hit the cap on everything). Starting with the 11th game, a characters growth rates will be boosted or dropped if they are behind or ahead of the "average" stats. Like the main example, this helps deal with the ''very'' annoying chance that a character gets "RNG Screwed", except this is enough to force a restart on an entire ''file'' in some cases.
* WordOfGod to the contrary, most players of ''PuzzleQuest: Challenge Of The Warlords'' believe that the game "nudges" all sort of random stats in its own favor. As many people complain about the computer's habit of chaining together 4/5 gem combos and extra turns, it's even more blatant in Spell Resistance, where an opponent with 2% resistance across the board will block approximately 15% of spells. The player, with the same stats, will be lucky to block one spell in hundreds.
* This trope is often brought up in {{MMORPG}}s, where many players believe that item drop rates can be mathematically calculated to determine how many monsters you must kill until you "should" find said item, by assuming that a 1% drop rate means that after you've killed a hundred, something's wrong if you haven't gotten one.
** Because of players complaining about this, the drop rate formula in ''WorldOfWarcraft'' was changed to ''increase'' the drop percentage every time the quest item required ''doesn't'' drop and reset it after one ''does'' drop. Of course, this is also to avoid the wild variation in time a quest can take when it's truly random.
** Indeed, while the mean number of kills is 100, the actual number will be greater than 100 37% of the time. Of course, this also means that 50% of the time it will require fewer than 70 kills.
* Inspeaking of ''WorldOfWarcraft'', during the famous "Leeroy Jenkins" video, someone is asked to do a number crunch to calculate their odds of finishing an encounter. [[PoesLaw It's actually not as simple as that - it was done to make fun of guilds]] as well as straw vulcans who may often rely on statistical fallacies.
* ''CityOfHeroes'' actually has a mechanic that behaves like the second part, called the "streakbreaker". For a given base percentage chance to hit, if a player or mob misses a certain number of times in a row, the next hit is guaranteed. For a hit chance below 20% you have to miss something like 100 times in a row, but for hit chances above 90%, it only takes one miss to get a guaranteed hit on the next attack. If you were paying REALLY close attention, you could use this to ensure that a key attack doesn't miss.
* DungeonFighterOnline has a dice roller that is perfectly random for the first instance of every sequence (first upgrade attempt, or random item pickup, or something similar), but then often produces identical results for the next several sets (Failing an identical upgrade five times in a row, the same player getting every single item in a dungeon). It often "corrects" itself and skews the other way until results are even. The hit/miss ratio is the same, either producing a lot of hits or a lot of misses in a row, only rarely looking like the actual statistic.
* The ''VideoGame/{{Tetris}}'' Guideline has mandated that all Tetris games since around late 2005 have an implementation to make the gambler's fallacy actually happen (and make players complain less of being screwed by the [[RandomNumberGod RNG]]): Instead of rolling a D7 to select a piece, newer Tetris games take a sequence of all seven pieces and deals random permutations of it. Thus, after every 7th piece, all seven have appeared with equal frequency. This also makes every 7th piece completely predictable.
** Prior to that, the ''TetrisTheGrandMaster'' series also had an algorithm to make the gambler's fallacy come true: The game rolls 6 times (4 in the first TGM) and takes the first result that isn't identical to any of the four most recent pieces dealt. It's still possible for this to "fail" and give you the same pieces over and over again since the game only rolls a fixed number of times; it's just much less likely than with a simple RNG approach.
*** The Tetris piece-picking algorithms are many and varied. One, the appropriately named Bastet system, [[SpitefulAI picks the worst piece possible for your current situation with an 85% accuracy.]]
* Ask anyone who's played ''{{Civilization}} IV'' (''especially'' those who play mods like ''FallFromHeaven'') and they will tell you that any combat with less than 80% odds is suicidal and should be avoided at all costs [[hottip:*:though this isn't purely for the chance weighting, as it effects how much your unit gets damaged, which combined with the AI favoring large stacks of weak units, means your unit will likely die next turn]], unless the odds are 1% or worse, in which case victory is surprisingly possible (see Spearman v. Tank).
** Alleviated somewhat in the sequel, which is kind enough to give you all of the information BEFORE you attack and provides a rough estimate of where the forces will end up in strength after the round of combat. It was actually criticized heavily for its near-perfect accuracy in prediction! Later patches actually made it a bit more random.
* This trope is hugely responsible for the ''{{Pokemon}}'' entries on TheComputerIsACheatingBastard, and is the number 1 thing the game's [[StopHavingFunGuys professional]] players complain about to similar levels of usage.
** In a more topical instance, players have a random 1/8192 chance of finding an alternately colored Pokemon, similar to albinism and what not. Many players only encounter one or two in several years of playing, others never find one, and some find them with surprising regularity.
** In a similar way, the Pokerus (a "virus" that doubles a Pokemon's stat growth) has a 3/65,536 chance to be on a Pokemon, or 1/3 the probability of finding a "shiny" Pokemon. Many players have never seen the Pokerus, while a few have been lucky enough to get it more than once. Once you have a Pokemon with the Pokerus, though, it's very easy to spread it around the party.
** The first generation did have statistical errors due to bugs, such as attacks that should never miss actually having a 1/256 chance of missing due to the code using "less than" checks instead of "less than or equal to" checks.
* ''[[MakaiToshiSaGa Final Fantasy Legend]]'', with the infamous Saw GameBreaker weapon. On the enemies it would work on at all, (see GameBreaker about the flaw making it work on too many enemies), it had a 50% chance of getting a OneHitKO. In practice, this meant that it would alternate between hitting and missing. Thus, if you wanted to use them in battle, just equip two different characters with them and have them both use it in a given round. If the first misses, the second would be guaranteed to hit.
* ''FinalFantasyTacticsA2'': many people report that attacks that give a 95% success rate fail often. It seems likely that this is the case given the number of complaints (especially since the previous game didn't have these problems) but obviously it's impossible to say for sure.
* ''{{X-COM}}'''s accuracy reports during combat aren't exactly blatant lies, but they're not exactly accurate, either. What ''X-COM'' does for a hit check is up to two rolls. The first is done against the accuracy check, and if it passes, you automatically get a dead-on shot. The other roll, if the first fails, is the deviation from where you're aiming, which may also end up being nil, resulting in a dead-on shot. So that 75% Accuracy the game reports? More like 77% to hit the target you're aiming at, and up to around 20% to hit someone else, resulting in somewhere around a 86% (on average) chance of someone getting hit by any given shot in a heated battle. Oh, and 100% accuracy reportedly doesn't exist.
* The MaddenCurse works this way. Generally, the cover is awarded to some athlete who just had a phenomenal season. The next season, the player is often beset by the sorts of bad luck that befall all athletes (injuries, bad games, etc) except they receive more attention. In some cases, it may also be a SelfFulfillingProphecy if the player gets a big ego and skimps on workouts, or if other players are more motivated to play hard against him. But mostly it's just that any season of a player is likely to be average (for his or her capabilities) and any season which leads to feature a player in games or magazine stories is likely to be way above average, so it's just a good chance of a "dice roll" showing a lower number, just like the next number after you rolled a 6 on a normal die is likely to be lower than that.
** A great example of this would be Brett Lorenzo Favre's appearance on Madden. It appeared that Favre had subverted, nay, broken the Madden curse while playing for the New York Jets. Then the Jets lost four straight games and a bid for the playoffs. "What went wrong?" you ask. Brett Favre played the last month of the season with a torn bicep in his throwing arm and no one did anything about it.
** The technical name for this is [[http://en.wikipedia.org/wiki/Regression_toward_the_mean regression toward the mean]].
** A more direct example are the year-in, year-out complaints that either the stats or the on-field experience are unrealistic, by pointing to the raw numbers. Since ''JohnMaddenFootball'' is a video game, the developers have to shorten the quarters because most gamers aren't willing to invest multiple hours on a single game. So ultimately this means that gamers are running between 50-70% as many plays as a real NFL contest. Yet many expect to produce as many points or exciting moments, while somehow maintaining realistic results on a per-play basis. This is mathematically impossible. EA chooses the former, heavily slanting the game in favor of the offense, which has caused somewhat of a BrokenBase amongst fans of the series.
* ''{{Warhammer 40000}}'': Fears of "bad dice" abound. The previously mentioned lack of even distribution and the tendency of rolling methods to influence the result only adds fuel to the fire.
* ''BloodBowl'': There's always a 1 in 6 chance of succeeding or failing because ones always fail and sixes always succeed. Players hate this because you tend to fail at the worst possible time. Failing also ends your turn in most cases, so superstition abounds.
** This is also the "rebuttal" of any claims of the AI cheating in the computer game based on it, not taking into account that the exact sequence of rolls is predetermined at the start of any given game (which they mention IN their rebuttal) and thus CAN BE LOOKED AT before they happen, thereby giving the AI an opportunity to cheat. [[{{Savescumming}} Of course, it also provides an avenue for players to cheat where save games are available...]]
* In ''{{A Song of Ice and Fire}}'' roleplaying system, there is a table for rolling random events in your family's history. This would be perfectly fine, except that you roll 3 dice for the events (thus making the events in the middle more likely), and the table is in ALPHABETICAL ORDER. Thus Doom (the worst thing that can possibly happen to a family) is more likely than a mere Catastrophe (still bad, but not even half as bad), just because Doom is closer to the middle of the list than Catastrophe is.
** [[CrapsackWorld In that example, the results are very true to the setting.]]
* In a strange twist, ''Final Fantasy VII: Crisis Core'' had the DMR, a slot-machine of various character faces that spins during combat, creating different effects. The only way to level-up is for three "7"s to align. Isn't that awful?!? Leveling based on total randomness?!? Except. . .it isn't. The manual ''lies''. The DMR is actually controlled by an ''insanely complicated'' mathematical formula that, in-game, manifests itself as the strange impression that chance always ''just so happens'' to work out exactly the way natural progression should. In essence, one in a million chances succeed nine times out of ten.
[[AC: {{Theater}}]]
* ''CoxAndBox'': In the (sometimes cut) gambling number, the titular characters roll nothing but sixes on their dice, leading them to suspect the other is cheating. Although they both ''are'', no dice-weighting is quite ''that'' good.
* Deconstructed in RosencrantzAndGuildensternAreDead by TomStoppard. A coin flipped nearly a hundred times comes up head each time, and they try to figure out how it's happening. Two explanations Guildenstern develops are divine intervention and random chance.
** Hamlet himself (though in his [[{{Hamlet}} own play]]) provides the in-universe explanation: "The time is out of joint". Presumably this affects the law of probability somehow.
[[AC:WebComics]]
* In ''DarthsAndDroids'', Pete (R2-D2) likes to "[[RandomNumberGod pre-roll the ones out]]" of his 20-sided dice. He takes a huge number of dice and rolls them once each, and selects the dice that rolled a one. He rolls those dice again, and selects the dice that rolled one a second time. Since the odds of any given d20 rolling a one three times in a row is 1 in 8,000, another roll of any of these dice has only a 1 in 8,000 chance of rolling a one again, right? ... No.
** When one of said dice ''does'' roll a 1... "Now it's even '''''luckier'''''!" [[hottip:*:Assuming the dice can be unbalanced, doing that with enough dice enough times will get you the ones that are ''prone'' to rolling ones.]]
*** Even better - his reason for pre-rolling is the fact that he doesn't believe in "lucky dice".
